Author
Jonathan Sacks
Bio: Jonathan Sacks is an academic researcher. The author has an hindex of 1, co-authored 1 publications receiving 873 citations.
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TL;DR: In this article, the authors define a parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J).
Abstract: Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called a (non-parametrized) J-curve in V. A curve C C V is called closed if it can be (holomorphically !) parametrized by a closed surface S. We call C regular if there is a parametrization f : S ~ V which is a smooth proper embedding. A curve is called rational if one can choose S diffeomorphic to the sphere S 2.
2,482 citations
08 Jun 2006
TL;DR: In this paper, the Korteweg de Vries equation was used for ground state construction in the context of semilinear dispersive equations and wave maps from harmonic analysis.
Abstract: Ordinary differential equations Constant coefficient linear dispersive equations Semilinear dispersive equations The Korteweg de Vries equation Energy-critical semilinear dispersive equations Wave maps Tools from harmonic analysis Construction of ground states Bibliography.
1,733 citations
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1,317 citations
1,125 citations
TL;DR: Soit X une u-variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee Q est definie positive.
Abstract: Soit X une u-variete compacte reguliere simplement connexe orientee avec la propriete que la forme associee Q est definie positive. Alors cette forme est equivalente, sur les entiers, a la forme diagonale standard, soit dans une base: Q(u 1 ,u 2 ,...u 2 )=u 2 1 +u 2 2 +...+u 2 2
899 citations